function name/domain

Im so confused !!

Q1:

A drug trial is studying the efficacy of a new drug for thalassemia, a genetic disorder in which a patient is unable to properly synthesize the hemoglobin molecule in the blood. In the trial, the rate at which the drug is metabolized by the body is studied. The data from the trial is then used to construct a model for the drugís metabolism. The concentration of a drug, in parts per million, in a patientís blood t hours after the drug is administered is given by the function :

f(t)=t^5+ 3t^4- 6t≥- 2t≤+ 60t
a) What type of function is used to model the drug concentration?

b) What is the appropriate domain for this function?

c) We would like to determine when the drug is completely eliminated from the bloodstream. Find this value of time, t. Explain why an exact solution to this problem is possible

for part (a) you can call it a polynomial function.
for part (b): in general setting you would say that the domain is R. In this case, since t is in hours, then the domain is .
for part (c): the objective is to find the value of t for which f(t) becomes zero. This happens only if t=0 which is not a logical answer. There must be something wrong with the given. Take a look at this: http://www.wolframalpha.com/input/?i=t^5%2B3*t^4-6*t^3-2*t^2%2B60*t